Question

5 -letter "words" are formed using the letters A, B, C, D, E, F,
G. How many such words are possible for each of the following
conditions?

a) No condition is imposed.

b) No letter can be repeated in a word.

c) Each word must begin with the letter A.

d) The letter C must be at the end.

e) The second letter must be a vowel.

Answer #1

a) Number of letters = 7

Number of 5 letter words possible, with no conditions imposed =

= **16,807**

b) Number of 5 letter words possible, with no repetition = 7P5

= 7!/(7-5)!

= 7 x 6 x 5 x 4 x 3

= **2520**

c) Number of 5 letters words possible if each word must begin with A = 1 x

= **2401**

d) Number of 5 letters words possible if the letter C must be at
the end = Number of 4 letter words without C x Number of options
for last letter

*(It is not necessary that the last letter is C)*

=

= **9072**

e) Number of options for second letter = 2 *(A and
E)*

Number of options for other 4 letters = 7

Number of words possible if the second letter must be a vowel =

= **4802**

a) How many four-letter words can be formed from the letters of
the word TAUDRY if each letter can only be used one time in a word?
Y is NOT considered a vowel in this word.
b) How many contain the letter Y?
c) How many contain all the vowels?
d) How many contain exactly three consonants?
e) How many of them begin and end in a consonant?
f) How. many begin with a D and end in a vowel...

a) How many four-letter words can be formed from the letters of
the word TAUDRY if each letter can only be used one time in a word?
Y is NOT considered a vowel in this word.
b) How many contain all the vowels?
c) How many contain exactly three consonants?
d) How many of them begin and end in a consonant?
e) How many contain both D and Y?

How many words can be formed by arranging the letters of the
word “EQUATIONS” such that the first letter of the word is a vowel
and the last position is a consonant letter? (Note: The words thus
formed need not be meaningful.)

(a) How many words with or without meaning, can be formed by
using all the letters of the word, ’DELHI’ using each letter
exactly once?
(b) How many words with or without meaning, can be formed by
using all the letters of the word, ’ENGINEERING’ using each letter
exactly once?

How many 3 letter words (both nonsense and sensical) may be
formed out of the letters of the word 'PROBABILITY'?
The choices given are:
a. 210
b. 432
c. 552
d. 531
e. 1960

In the problems below, A and B can be repeated.
(a) How many 10 letter words can be formed using the letters A and
B? (b) How many of these 10 letter words contain at most 2 A’s?

Consider lists of length 6 made from the letters A, B, C, D, E,
F, G, H. How many such lists are possible if repetition is not
allowed and the list contains two consecutive vowels?
How many integers between 1 and 1000 are divisible by 5? How
many are not divisible by 5?
How many integers between 1 and 9999 have no repeated digits?
How many have at least one repeated digit?

How many different 6-letter radio station call letters can be
made a. if the first letter must be G or X and no letter may be
repeated? b. if repeats are allowed (but the first letter is G or
X)? c. How many of the 6-letter radio station call letters
(starting with G or X) have no repeats and end with the letter
R?

1. (4 pts) Consider all bit strings of length six. a) How many
begin with 01? b) How many begin with 01 and end with 10? c) How
many begin with 01 or end with 10? d) How many have exactly three
1’s? 2. (8 pts) Suppose that a “word” is any string of six letters.
Repeated letters are allowed. For our purposes, vowels are the
letters a, e, i, o, and u. a) How many words are there? b)...

How many “words” are there of length 4, with distinct letters,
from the letters {a, b, c, d, e, f}, in which the letters appear in
increasing order alphabetically. A word is any ordering of the six
letters, not necessarily an English word.

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